Volume of Revolution via Shells | MIT 18.01SC Single Variable Calculus, Fall 2010

[@mpcc2022]

This was the simplest and most coherent explanation I've heard

[@evangrove599]

Agreed. I've watched 5 videos and this made the most sense.

[@LaneSurface]

In case anyone is interested in solving with the washer method: - Choose to integrate with respect to y. - Find the functions in terms of y. For y=sqrt(x), this becomes x=y^2. - The area of the cross-section is given by the difference between the inner circle and outer (which is x=6-y^2). This becomes A(y)=pi*(6-y^2)^2-pi*(6-4)^2=pi*(y^4-12y^2+36-4)=pi*(y^4-12y^2+32). - The lower bound a is given by the x-axis or y=0. That is, a=0. The upper bound is given by the value of y at the right-most limit of the region. Thus, y=sqrt(4)=2 is the upper bound b=2. - Integrating gives pi*int_0^2[y^4-12y^2+32] dy. Solving gives 192*pi/5, the same result obtained in this video.

[@ainmiky4620]

when my prof explained this it was soooooo hard. You made it so simple. I'ts not fair MIT has these teachers huuhuuh

[@cosmichasm]

now why couldn't my professor have put it that way

[@HeyKevinYT]

Whoever operated the camera did a good job zooming in and out views for convenience

[@goldengal1989]

This is one of the best calculus videos that I've seen on KZbin.

[@enyioma8]

I like this professor. Teaches really well

[@pa800korg92]

Very simply put, clear explanation, thank you!

[@mohamedmilad4235]

I love the way how you explained it

[@MrsCullenx52]

i wish my calculus teacher explained this half as well as you do! thanks so much.

[@EngHussain700]

الله عليج يا فخر اوروبا مدري امريكا على هذا الشرح الرائع

[@lithiumnode]

The exact answer to the problem is 192π/5 ... or yes, roughly 120.637.

[@RichieRussell23]

Thank you!

[@ouextica]

I wish MIT was my university.

[@joelmaim8925]

Wow Ma'am, your tutorial was so clear!

[@georgesadler7830]

I really understand this Volume method using shells, however drawing a picture is very important before solving this or any related problem.

[@tahy59]

astonishing ,absolutely amazing

[@manthanchandrabhargav6039]

Thank you for the simplest explanation.

[@twlson49]

very good explanation.. I enjoyed that ... I have a limited understanding of calculus but I came away with something very intuitive

[@alsaineybarry-wu9yt]

I struggle alot while my lecturer was explaining this but it seems like drinking a cold water to me 😊

[@psyberion]

Sorry I was only referring to the integral between the limits x=0 and x=4, so really overall by my calculation I get: 2 . pi . 19.2 (approx. 120.637).

[@vanlam8929]

Best Explaination !

[@mikeearls126]

I think to be a math professor at MIT you need to be a real pro

[@markweiler4965]

You could use this to find the entrance to a wormhole

[@not_amanullah]

Thanks ❤️🤍

[@drewpasttenseofdraw]

JMT doesn't explain maffs he works problems.

[@moonbabies]

I know it's late but that's the equation for a cylinder.

[@musawaleed224]

Excellent explanation thanks very much

[@Algebrainiac]

This topic was the death of me in calculus 💀💀💀

[@Shadow-vu7tq]

If I had a kid going to college I'd would want some Video of their lecture styles to decide which college to go to there are hacks out there

[@6subswith0vids80]

Wtf are you saying lmao

[@Shadow-vu7tq]

@@6subswith0vids80 not talking about mit I watch a few math videos there is a difference in a lecturers styles some of these posters are just looking for KZbin cash

[@sk99gaming99]

i would use disc method tbh.. its easy and we already have the points

[@studiant3004]

Very good didatic video

[@psyberion]

Cool, thanks for the confirmation.

[@Jho1802]

Thank u ante lab you

[@mbenitez6722]

She is so sweet and clear! ^__^

[@laouhai174]

thank you very much

[@joseangeluruetaperez4310]

VERY GOOD NICE TEACHER

[@jamshidabdullayev4952]

Thank you

[@pandaindistress4728]

If someone sees this , can someone explain why the r=6- x and not r=6-squareroot of x ??

[@Guitarsg62]

Thank you! :)

[@j2a929]

i understand better from this i just don't get my own Korean professor's words

[@400080vikkash]

my math teacher makes us solve the y= for x when we are rotating about the y axis I don't understand why? seems like you didn't that that here

[@Antymills424]

Thanks!

[@UtkarshGuptaBES]

192pi/5

[@jacobskarby1389]

I got the volume to be about 268 units; anyone else?

[@candyfruit7426]

Tysm😊😊☺️

[@henryjunior38]

Patrickjmt is the master

[@richard7957]

Dear Christine good explanation ...but what about using a lightboard in your math classes?

[@swedishpsychopath8795]

Or better use a ouija -board to understand this ....

[@batusulun7297]

What would we be the radius if we used disk method?

[@orwakharraz]

great thank you

[@jamshidabdullayev4952]

Thank you

[@vince2344]

Are you suppose to subtract the volume of the cylinder inside x=4 and x=6 if you'll use that formula?

[@christopherrichardson5565]

why she did 6-x instead of 6-(sqrt x) for radius

[@drewpass5697]

because sqrt(x) represents just the height of the "region" (or the top part of the region that looks like half a parabola). The 'x' is just any arbitrary x value which I like to think of it as the "width portion" of the region (it's arbitrary because depending on where we draw the slice, or rectangle, x can be any value that is between 0 and 4 on the x-axis). I know I'm not using the correct terminology here but I think of it this way. The radius is sort of like the width portion and the equation of the curve y=sqrt(x) is sort of like the height portion. Since the axis of rotation is at a fixed x value (the value x = 6), then the distance for the radius of the region to the axis of rotation would be 6 - x. Sorry but this probably only confused you more. I know this isn't the best explanation :(

[@haesoljung3587]

this is why i want to go to mit lol

[@Aguvika]

why do we not get the same volume if we rotate about x = -2? The inner radius of 2 units is maintained and we go from 0 to 4. Should we not get the same volume?? in this case r = 2+x

[@masonmunkey6136]

logically rotating about x=-2 should have a greater volume because the taller part of the graph is on the outside and moves farther

[@adrians.v.s.k2777]

y=0, then x=0??? shouldn't 0 be on the y-axis? why did tou put on the x-axis? can anyone explain this to me please?

[@drewpass5697]

The equation is y = 0 and this is a horizontal line. All the points on the x-axis are of the form (x, 0), meaning they are all the points on a horizontal line which have the y-coordinate being zero. Had it been x = 0 this would've been the y-axis since x = 0 would represent the vertical line in which all the points are of the form (0, y). In broad terms, any equation of the form y = b, where b is some number, represents a horizontal line in which all the points are of the form (x, b). The equation x = a, where a is some number, represents a vertical line in which all the points are of the form (a, y).

[@Ebra72]

So... ever heard of PatrickJMT ;)?

[@psyberion]

Has anyone completed the calculation? I get 19.2, is this correct?

[@sodaxcandy08]

i mean 2+x

[@arsalanwani2436]

Maam..i want to see complete course

[@mitocw]

View the complete course at: ocw.mit.edu/18-01SCF10. Best wishes on your studies!

[@arsalanwani2436]

@@mitocw i visited on this site..but no video is shown there..

[@mitocw]

The videos are on the pages in each section. Did you want the KZbin playlist? KZbin playlist: kzbin.info/aero/PL590CCC2BC5AF3BC1.

[@mk16ification]

If x=1 would you the height be sqroot of x - 1?

[@ishansinha1336]

ans is 80pi ?

[@sulaimanahsan6651]

if we subtract x-6 then ???

[@rajankandel8354]

take modulus sign

[@pinkybananas1]

is r always the axis or rotation minus the point where you are??

[@bamboozi]

+pinkybananas1 r is always the distance to the axis of rotation.

[@waliagovind]

She teaches at MIT. Do you think that might have something to do with it, instead of her sex?

[@Cyroavernus]

and KhanAcademy!!!

[@sodaxcandy08]

can the radius also be 2-x?????

[@AlfaHanen1]

nice

[@hahaha10001]

wait where did you get the 2pirh?

[@not_amanullah]

This is helpful ❤️🤍

[@jester60ify]

What does h stands for?

[@Gross126]

do you have disk method?

[@santiagocortes7964]

👏

[@jhonmicla7905]

Sir, i'm studying Civil engr and soon to be taken aN exam and now iam reviewing a kindof problem that its hard for me.. would you like to help me this this kind of problem? this is the question. A RECTANGULAR WHOSE WIDTH IS 4 UNITS AND HEIGHT IS 2 UNITS HAS ITS CENTER AT COORDINATE OF (10,12) THE 4 UNITS SIDE IS PARALLEL TO THE Y AXIS. FIND THE VOLUME OF GENERATED BY REVOLVING THE AREA ABOUT THE Y-AXIS. THANKS

[@ranblake3165]

Audio

[@crashmoneymusic1]

#justiceforzafir

[@alexjackson1130]

Too hard miss, can I do some sums instead

[@montrealmathandphysicstuto2807]

I believe that this can be solved easier by the disks method. And as with the majority of videos in this topic you fail to address the reason where we have no option but to use the shells method.

[@srikarvalluri9621]

She didn't say that! 2:51

[@josephdominguez4219]

Your ok but you break at the universe level

[@mittmasai1678]

I have watched patrickjmt AND christine Brener is the better.Of cause it depends on your IQ.

[@kenichimori8533]

Topology 0 Point bin the shell 0/P/P/

[@ranblake3165]

Audio